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> ### Test nlsBootPredict() on a linear model
> library(nlstools)

'nlstools' has been loaded.

IMPORTANT NOTICE: Most nonlinear regression models and data set examples
related to predictive microbiolgy have been moved to the package 'nlsMicrobio'

> set.seed(123)
> n <- 30
> x <- rnorm(n)
> eps <- 0.3 * rnorm(n)
> d <- data.frame(x = x, y = x + eps)
> model <- lm(y ~ x, data = d)
> new <- data.frame(x = seq(-3, 3, 0.1))
> pred.plim <- predict(model, new, interval = "prediction")
> pred.clim <- predict(model, new, interval = "confidence")
> plot(y ~ x, data = d)
> abline(model)
> lines(new$x, pred.clim[, 2], pch = 19, col = "red")
> lines(new$x, pred.clim[, 3], pch = 19, col = "red")
> lines(new$x, pred.plim[, 2], pch = 19, col = "blue")
> lines(new$x, pred.plim[, 3], pch = 19, col = "blue")
> 
> # using nls
> formu <- as.formula(y ~ a + b *x)
> nlsmodel <- nls(formu, start = list(a = 0, b = 1), data = d)
> niter <- 200
> # niter <- 2000
> nlsboot <- nlsBoot(nlsmodel, niter = niter)
> (pred.clim <- nlsBootPredict(nlsboot, newdata = new, interval = "confidence"))
           Median        2.5%       97.5%
 [1,] -2.81723283 -3.06886491 -2.56176657
 [2,] -2.72240073 -2.96521056 -2.47398234
 [3,] -2.62688270 -2.86155621 -2.38619811
 [4,] -2.53181770 -2.75790186 -2.29841389
 [5,] -2.43797866 -2.65424751 -2.21062966
 [6,] -2.34207290 -2.55059316 -2.12284543
 [7,] -2.24502643 -2.44693881 -2.03506121
 [8,] -2.14756496 -2.34328446 -1.94727698
 [9,] -2.04807972 -2.23963011 -1.85949275
[10,] -1.95017795 -2.13597576 -1.77170853
[11,] -1.85723345 -2.03226366 -1.68392430
[12,] -1.76459035 -1.92879542 -1.59614007
[13,] -1.66806241 -1.82883128 -1.50835585
[14,] -1.57155165 -1.72886715 -1.42057162
[15,] -1.47506156 -1.62890302 -1.33128494
[16,] -1.38158668 -1.52893888 -1.24092639
[17,] -1.28732055 -1.42498548 -1.15056784
[18,] -1.19193012 -1.32152294 -1.06160823
[19,] -1.09736481 -1.22061195 -0.97290652
[20,] -1.00410625 -1.12302497 -0.88187157
[21,] -0.90745624 -1.02483214 -0.79083661
[22,] -0.81031137 -0.92406432 -0.69980166
[23,] -0.71505169 -0.82627502 -0.60876670
[24,] -0.61889962 -0.72841827 -0.51773174
[25,] -0.52157624 -0.62623433 -0.42983868
[26,] -0.42683848 -0.52394020 -0.33735571
[27,] -0.33118873 -0.42326139 -0.24609849
[28,] -0.23786960 -0.32492441 -0.15449917
[29,] -0.14332530 -0.22215654 -0.06509836
[30,] -0.04585133 -0.12859456  0.03399433
[31,]  0.05058588 -0.03043206  0.13318525
[32,]  0.14705772  0.06766891  0.22733001
[33,]  0.24119613  0.16446070  0.32344443
[34,]  0.33755519  0.25427284  0.42300254
[35,]  0.43214403  0.34667850  0.52256065
[36,]  0.52647995  0.43317279  0.62208172
[37,]  0.62390411  0.52448037  0.72157104
[38,]  0.72079144  0.61985771  0.82117664
[39,]  0.81411689  0.71096015  0.92079309
[40,]  0.91012841  0.80206260  1.02111009
[41,]  1.00785607  0.89268696  1.12215759
[42,]  1.10218544  0.98412098  1.22320508
[43,]  1.19951544  1.07508127  1.32428941
[44,]  1.29468570  1.16604155  1.42539870
[45,]  1.39116797  1.25513984  1.52761939
[46,]  1.48527700  1.34198474  1.62953524
[47,]  1.58047608  1.42886857  1.73441227
[48,]  1.67468220  1.51575240  1.83759862
[49,]  1.76869460  1.60257838  1.94078498
[50,]  1.86463717  1.68928230  2.04397134
[51,]  1.96049585  1.77598622  2.14715769
[52,]  2.05618626  1.86273760  2.25024088
[53,]  2.15312465  1.94958776  2.35329727
[54,]  2.24875449  2.03643792  2.45635366
[55,]  2.34387805  2.12328807  2.55772073
[56,]  2.43967975  2.21084405  2.65792040
[57,]  2.53711007  2.30020056  2.76324790
[58,]  2.63340424  2.38955707  2.86887040
[59,]  2.72959131  2.47554498  2.97208648
[60,]  2.82530730  2.56103654  3.07530257
[61,]  2.92142186  2.64652811  3.17851865
> (pred.plim <- nlsBootPredict(nlsboot, newdata = new, interval = "prediction"))
           Median        2.5%       97.5%
 [1,] -2.81156029 -3.31437355 -2.27764257
 [2,] -2.73771552 -3.27981895 -2.18539695
 [3,] -2.63525405 -3.08939408 -2.09519587
 [4,] -2.57005016 -2.95515841 -1.97747747
 [5,] -2.46821618 -2.93303625 -1.96016775
 [6,] -2.39178847 -2.86568046 -1.68223035
 [7,] -2.25212430 -2.74238984 -1.78353859
 [8,] -2.21657017 -2.65896935 -1.59621918
 [9,] -2.02554499 -2.56086884 -1.58921698
[10,] -1.95530358 -2.46666009 -1.49606581
[11,] -1.90786850 -2.29507605 -1.28546905
[12,] -1.79722318 -2.22052568 -1.14699796
[13,] -1.70311397 -2.18837023 -1.05472323
[14,] -1.60066569 -2.05463643 -0.98507056
[15,] -1.48792163 -1.91809896 -0.91807750
[16,] -1.42888777 -1.86901978 -0.87050450
[17,] -1.28693880 -1.74373558 -0.86112798
[18,] -1.22557919 -1.60290108 -0.70156863
[19,] -1.13583961 -1.59088200 -0.61161767
[20,] -0.99427412 -1.46211770 -0.38928708
[21,] -0.91306506 -1.39666339 -0.43015214
[22,] -0.85403742 -1.24949895 -0.40943922
[23,] -0.74452951 -1.22090440 -0.30023989
[24,] -0.67605355 -1.08107391 -0.22231932
[25,] -0.56940429 -0.95688978  0.01514277
[26,] -0.44164002 -0.87614760 -0.05747353
[27,] -0.33143112 -0.77537022  0.26876255
[28,] -0.30696583 -0.68657377  0.17819028
[29,] -0.16520093 -0.60708025  0.26980506
[30,] -0.12390914 -0.51478356  0.31114975
[31,] -0.01433719 -0.40848685  0.43599896
[32,]  0.07598464 -0.32474756  0.68950435
[33,]  0.21914024 -0.25065051  0.86040954
[34,]  0.27235729 -0.10333262  0.90631235
[35,]  0.43987253  0.01959801  1.01438291
[36,]  0.45197515  0.10601563  1.14321731
[37,]  0.55916984  0.14634499  1.02231898
[38,]  0.65269608  0.26571445  1.20396295
[39,]  0.77528177  0.37415362  1.34427761
[40,]  0.88063381  0.45589500  1.32525205
[41,]  1.02191172  0.55514687  1.56833146
[42,]  1.06086132  0.64000747  1.65307906
[43,]  1.15390947  0.71974206  1.77641620
[44,]  1.27921488  0.89752021  1.78938867
[45,]  1.39386996  0.95918537  1.94016941
[46,]  1.48498235  1.04131152  1.97068130
[47,]  1.55316657  1.04122912  2.08435371
[48,]  1.64948805  1.15138646  2.15021618
[49,]  1.76940691  1.37131105  2.31602033
[50,]  1.84076275  1.40577238  2.45304957
[51,]  1.90693000  1.46021705  2.43589689
[52,]  2.06220192  1.60483896  2.72860268
[53,]  2.16668163  1.66909986  2.74461269
[54,]  2.22338747  1.75824779  2.86996867
[55,]  2.29596473  1.94881227  2.90885518
[56,]  2.44366609  1.94934694  2.93433809
[57,]  2.48361793  2.00899269  3.01496469
[58,]  2.66475825  2.13613039  3.22360952
[59,]  2.78338227  2.18512024  3.30968447
[60,]  2.82765555  2.30179900  3.42300120
[61,]  2.93908539  2.34957865  3.59145763
> 
> lines(new$x, pred.clim[, "2.5%"], pch = 19, col = "red", lwd = 2, lty = 2)
> lines(new$x, pred.clim[, "97.5%"], pch = 19, col = "red", lwd = 2, lty = 2)
> lines(new$x, pred.plim[, "2.5%"], pch = 19, col = "blue", lwd = 2, lty = 2)
> lines(new$x, pred.plim[, "97.5%"], pch = 19, col = "blue", lwd = 2, lty = 2)
> 
> ### Use of nlsBootPredict() a non linear model 
> data(vmkm)
> nls1 <- nls(michaelis,vmkm,list(Km=1,Vmax=1))
> plotfit(nls1, smooth = TRUE)
> 
> nlsb1 <- nlsBoot(nls1, niter = niter)
> new1 <- data.frame(S = seq(0.3, 2, 0.1))
> (pred.clim <- nlsBootPredict(nlsb1, newdata = new1, interval = "confidence"))
         Median      2.5%     97.5%
 [1,] 0.1608109 0.1509141 0.1727522
 [2,] 0.2073174 0.1955793 0.2206870
 [3,] 0.2507233 0.2377474 0.2650256
 [4,] 0.2913338 0.2775170 0.3066177
 [5,] 0.3297796 0.3151818 0.3452034
 [6,] 0.3659105 0.3509235 0.3805432
 [7,] 0.3993828 0.3855575 0.4127916
 [8,] 0.4313941 0.4185898 0.4446739
 [9,] 0.4618000 0.4491425 0.4743594
[10,] 0.4904356 0.4770375 0.5026707
[11,] 0.5171692 0.5032976 0.5310446
[12,] 0.5430686 0.5285592 0.5563806
[13,] 0.5674258 0.5524375 0.5806221
[14,] 0.5909129 0.5755214 0.6060323
[15,] 0.6129958 0.5971787 0.6297974
[16,] 0.6340656 0.6175658 0.6519336
[17,] 0.6542444 0.6358989 0.6748199
[18,] 0.6733062 0.6532512 0.6962930
> (pred.plim <- nlsBootPredict(nlsb1, newdata = new1, interval = "prediction"))
         Median      2.5%     97.5%
 [1,] 0.1608731 0.1132890 0.2116213
 [2,] 0.2070677 0.1592908 0.2611559
 [3,] 0.2514852 0.2016383 0.3045645
 [4,] 0.2933006 0.2386858 0.3376569
 [5,] 0.3295287 0.2789410 0.3686969
 [6,] 0.3655752 0.3154331 0.4258422
 [7,] 0.4005530 0.3535601 0.4564297
 [8,] 0.4310858 0.3829141 0.4871092
 [9,] 0.4611489 0.4105682 0.5213850
[10,] 0.4911382 0.4438490 0.5470805
[11,] 0.5151841 0.4659091 0.5670586
[12,] 0.5440623 0.4968048 0.6022715
[13,] 0.5665871 0.5174057 0.6238999
[14,] 0.5918079 0.5402556 0.6436058
[15,] 0.6122645 0.5609896 0.6670848
[16,] 0.6344426 0.5836094 0.6918973
[17,] 0.6558639 0.6010505 0.7115876
[18,] 0.6721842 0.6202672 0.7369739
> 
> lines(new1$S, pred.clim[, "2.5%"], pch = 19, col = "red", lwd = 2, lty = 2)
> lines(new1$S, pred.clim[, "97.5%"], pch = 19, col = "red", lwd = 2, lty = 2)
> lines(new1$S, pred.plim[, "2.5%"], pch = 19, col = "blue", lwd = 2, lty = 2)
> lines(new1$S, pred.plim[, "97.5%"], pch = 19, col = "blue", lwd = 2, lty = 2)
> 
> ### Use of nlsBootPredict() on a model with two independent variables
> data(vmkmki)
> nls2 <- nls(compet_mich, vmkmki, list(Km=1,Vmax=20,Ki=0.5))
> plotfit(nls2, variable=1)
> nlsb2 <- nlsBoot(nls2, niter = niter)
> # Define a new dataframe with a fixed value of one of the independent variable
> new2 <- data.frame(S = seq(0, 200, length.out = 50), I = rep(20, 50))
> (pred.clim <- nlsBootPredict(nlsb2, newdata = new2, interval = "confidence"))
         Median      2.5%     97.5%
 [1,]  0.000000  0.000000  0.000000
 [2,]  2.229075  1.964014  2.505346
 [3,]  3.965738  3.555823  4.375876
 [4,]  5.354522  4.879420  5.825738
 [5,]  6.505401  5.979054  6.983076
 [6,]  7.465570  6.920498  7.955946
 [7,]  8.275283  7.733432  8.751216
 [8,]  8.970185  8.441740  9.414154
 [9,]  9.569839  9.064398  9.987621
[10,] 10.098104  9.599816 10.491223
[11,] 10.555800 10.061758 10.937895
[12,] 10.968567 10.473366 11.347157
[13,] 11.346909 10.875290 11.727552
[14,] 11.685760 11.198077 12.050186
[15,] 11.991060 11.480176 12.351816
[16,] 12.263835 11.756363 12.658216
[17,] 12.507935 12.008256 12.916669
[18,] 12.744018 12.222000 13.141986
[19,] 12.954766 12.426739 13.361690
[20,] 13.148448 12.615910 13.572899
[21,] 13.333774 12.804298 13.759353
[22,] 13.504555 12.992251 13.930505
[23,] 13.658966 13.155973 14.095090
[24,] 13.807970 13.299565 14.245012
[25,] 13.945484 13.424567 14.385361
[26,] 14.073855 13.533892 14.517291
[27,] 14.193626 13.636401 14.641238
[28,] 14.308591 13.732711 14.757907
[29,] 14.411881 13.835735 14.867920
[30,] 14.508574 13.933486 14.977025
[31,] 14.603692 14.024380 15.085697
[32,] 14.697277 14.101632 15.188795
[33,] 14.777074 14.174832 15.286738
[34,] 14.858842 14.244292 15.379904
[35,] 14.939895 14.310291 15.468632
[36,] 15.008791 14.373081 15.553234
[37,] 15.074873 14.432890 15.627097
[38,] 15.141404 14.490021 15.700052
[39,] 15.205895 14.541330 15.773152
[40,] 15.268470 14.587407 15.843136
[41,] 15.330931 14.631452 15.910199
[42,] 15.387727 14.673597 15.974519
[43,] 15.445724 14.722060 16.036262
[44,] 15.501432 14.769568 16.095579
[45,] 15.554985 14.815204 16.152611
[46,] 15.607016 14.859076 16.207486
[47,] 15.659084 14.901284 16.260326
[48,] 15.707870 14.941941 16.311242
[49,] 15.754209 14.978260 16.360336
[50,] 15.796139 15.012992 16.407704
> (pred.plim <- nlsBootPredict(nlsb2, newdata = new2, interval = "prediction"))
           Median       2.5%     97.5%
 [1,] -0.02823239 -4.6796892  2.300498
 [2,]  2.23988020 -2.4610981  4.180531
 [3,]  4.03047429 -0.2730675  6.414034
 [4,]  5.52789874  0.5575357  7.928287
 [5,]  6.68569359  2.0075501  8.968554
 [6,]  7.60314026  3.2221837  9.698371
 [7,]  8.44784141  3.2101837 10.590407
 [8,]  9.01537699  4.5710485 11.533643
 [9,]  9.74755605  5.2898349 11.762063
[10,] 10.14661468  5.7804012 12.703409
[11,] 10.59862844  6.3850096 12.352637
[12,] 11.08462408  6.7354124 13.201548
[13,] 11.42194521  6.4875500 13.493741
[14,] 11.81036466  7.9775168 14.065000
[15,] 12.11941906  7.8355846 14.483614
[16,] 12.39492332  7.9310672 14.453802
[17,] 12.70962864  8.0828245 15.178719
[18,] 12.75944521  7.8138912 14.875768
[19,] 13.08234420  8.3194057 15.277659
[20,] 13.37378021  9.1323991 15.609978
[21,] 13.49241554  8.5067203 15.774638
[22,] 13.49576424  8.4338337 16.035849
[23,] 13.80516762  8.6570890 16.059327
[24,] 14.04334657 11.2241878 16.318820
[25,] 13.98801553  9.9748788 16.452846
[26,] 14.42058255 10.5225994 16.614654
[27,] 14.31375903  9.9244092 16.754540
[28,] 14.47231626  9.8332919 16.740688
[29,] 14.61017495  9.9023478 16.397990
[30,] 14.75729082 10.0015352 16.649989
[31,] 14.64862466 10.5641991 17.411711
[32,] 14.70121861 10.0548378 17.284624
[33,] 14.79272477 10.5636470 16.964207
[34,] 15.00099123 11.1700228 16.895946
[35,] 15.16623125 10.4803098 17.492793
[36,] 15.10861103 10.7964766 17.593089
[37,] 15.39438961  9.8479320 17.150725
[38,] 15.33274682 11.6535831 17.551700
[39,] 15.29669078 10.9813625 17.796919
[40,] 15.46281695 10.1845532 17.698473
[41,] 15.49241761 10.9351275 18.234832
[42,] 15.37161823 10.4486275 17.965742
[43,] 15.62841446 10.3465026 17.877197
[44,] 15.57961100 10.9049824 17.996772
[45,] 15.62867122 10.9045776 17.953193
[46,] 15.71784187 10.7934857 17.884115
[47,] 15.76231069 10.7309725 17.770117
[48,] 15.69185738 10.7586563 17.699649
[49,] 15.74437127 10.6136744 18.027233
[50,] 15.96582240 11.7123818 18.094859
> 
> plot(new2$S, pred.clim[, "Median"], type = "l", col = "black", lwd = 2, lty = 2)
> lines(new2$S, pred.clim[, "2.5%"], pch = 19, col = "red", lwd = 2, lty = 2)
> lines(new2$S, pred.clim[, "97.5%"], pch = 19, col = "red", lwd = 2, lty = 2)
> lines(new2$S, pred.plim[, "2.5%"], pch = 19, col = "blue", lwd = 2, lty = 2)
> lines(new2$S, pred.plim[, "97.5%"], pch = 19, col = "blue", lwd = 2, lty = 2)
> 
> 
> proc.time()
   user  system elapsed 
   1.20    0.10    1.26